Electron density retrieval from truncated Radio Occultation GNSS data

This paper summarizes the definition and validation of two complementary new strategies, to invert incomplete Global Navigation Satellite System Radio-Occultation (RO) ionospheric measurements, such as the ones to be provided by the future EUMETSAT Polar System Second Generation. It will provide RO measurements with impact parameter much below the Low Earth Orbiters' height (817 km): from 500 km down approximately. The first presented method to invert truncated RO data is denoted as Abel-VaryChap Hybrid modeling from topside Incomplete Global Navigation Satellite System RO data, based on simple First Principles, very precise, and well suited for postprocessing. And the second method is denoted as Simple Estimation of Electron density profiles from topside Incomplete RO data, is less precise, but yields very fast estimations, suitable for Near Real-Time determination. Both techniques will be described and assessed with a set of 546 representative COSMIC/FORMOSAT-3 ROs, with relative errors of 7% and 11% for Abel-VaryChap Hybrid modeling from topside Incomplete Global Navigation Satellite System RO data and Simple Estimation of Electron density profiles from topside Incomplete RO data, respectively, with 20 min and 15 s, respectively, of computational time per occultation in our Intel I7 PC.Peer ReviewedPostprint (published version

The Impact of Fat Tails on Equilibrium Rates of Return and Term Premia

We investigate the impact of ignoring fat tails observed in the empirical distributions of macroeconomic time series on the equilibrium implications of the consumption-based asset-pricing model with habit formation. Fat tails in the empirical distributions of consumption growth rates are modeled as a dampened power law process that nevertheless guarantees finiteness of moments of all orders. This renders model-implied mean equilibrium rates of return and equity and term premia finite. Comparison with a benchmark Gaussian process reveals that accounting for fat tails lowers the model-implied mean risk-free rate by 20 percent, raises the mean equity premium by 80 percent and the term premium by 20 percent, bringing the model implications closer to their empirically observed counterparts.pricing model, habit formation, term premium, equity premium, fat tails, dampened power law

Fully-Coupled Simulation of Cosmic Reionization. I: Numerical Methods and Tests

We describe an extension of the Enzo code to enable fully-coupled radiation hydrodynamical simulation of inhomogeneous reionization in large $\sim (100 Mpc)^3$ cosmological volumes with thousands to millions of point sources. We solve all dynamical, radiative transfer, thermal, and ionization processes self-consistently on the same mesh, as opposed to a postprocessing approach which coarse-grains the radiative transfer. We do, however, employ a simple subgrid model for star formation which we calibrate to observations. Radiation transport is done in the grey flux-limited diffusion (FLD) approximation, which is solved by implicit time integration split off from the gas energy and ionization equations, which are solved separately. This results in a faster and more robust scheme for cosmological applications compared to the earlier method. The FLD equation is solved using the hypre optimally scalable geometric multigrid solver from LLNL. By treating the ionizing radiation as a grid field as opposed to rays, our method is scalable with respect to the number of ionizing sources, limited only by the parallel scaling properties of the radiation solver. We test the speed and accuracy of our approach on a number of standard verification and validation tests. We show by direct comparison with Enzo's adaptive ray tracing method Moray that the well-known inability of FLD to cast a shadow behind opaque clouds has a minor effect on the evolution of ionized volume and mass fractions in a reionization simulation validation test. We illustrate an application of our method to the problem of inhomogeneous reionization in a 80 Mpc comoving box resolved with $3200^3$ Eulerian grid cells and dark matter particles.Comment: 32 pages, 23 figures. ApJ Supp accepted. New title and substantial revisions re. v

The Formation Rates of Population III Stars and Chemical Enrichment of Halos during the Reionization Era

[abridged] The First Stars in the Universe form out of pristine primordial gas clouds that have been radiatively cooled to a few hundreds of degrees Kelvin either via molecular or atomic (Lyman-Alpha) hydrogen lines. This primordial mode of star formation is eventually quenched once radiative and/or chemical (metal enrichment) feedbacks mark the transition to Population II stars. In this paper we present a model for the formation rate of Population III stars based on Press-Schechter modeling coupled with analytical recipes for gas cooling and radiative feedback. Our model also includes a novel treatment for metal pollution based on self-enrichment due to a previous episode of Population III star formation in progenitor halos. With this model we derive the star formation history of Population III stars, their contribution to the re-ionization of the Universe and the time of the transition from Population III star formation in minihalos to that in more massive halos where atomic hydrogen cooling is also possible. We consider a grid of models highlighting the impact of varying the values for the free parameters used, such as star formation and feedback efficiency. The most critical factor is the assumption that only one Population III star is formed in a halo. In this scenario, metal free stars contribute only to a minor fraction of the total number of photons required to re-ionize the universe. In addition, metal free star formation is primarily located in minihalos and chemically enriched halos become the dominant locus of star formation very early in the life of the Universe, at redshift z~25. If instead multiple metal free stars are allowed to form out of a single halo, then there is an overall boost of Population III star formation, with a consequent significant contribution to the re-ionizing radiation budget.Comment: 31 pages, 8 figures, ApJ accepte

The Era of Massive Population III Stars: Cosmological Implications and Self-Termination

The birth and death of the first generation of stars have important implications for the thermal state and chemical properties of the intergalactic medium (IGM) in the early universe. Sometime after recombination, the neutral, chemically pristine gas was reionized by ultraviolet photons emitted from the first stars, but also enriched with heavy elements when these stars ended their lives as energetic supernovae. Using the results from previous high-resolution cosmological simulations of early structure formation that include radiative transfer, we show that a significant volume fraction of the IGM can be metal-polluted, as well as ionized, by massive Population III stars formed in small-mass (10^6-10^7 Msun) halos early on. If most of the early generation stars die as pair-instability supernovae with energies up to 10^{53} ergs, the volume-averaged mean metallicity will quickly reach Z ~ 10^{-4}Zsun by a redshift of 15-20, possibly causing a prompt transition to the formation of a stellar population that is dominated by low-mass stars. In this scenario, the early chemical enrichment history should closely trace the reionization history of the IGM, and the end of the Population III era is marked by the completion of reionization and pre-enrichment by z=15. We conclude that, while the pre-enrichment may partially account for the ``metallicity-floor'' in high-redshift Lyman-alpha clouds, it does not significantly affect the elemental abundance in the intracluster medium.Comment: Version accepted by ApJ. Minor revisions and a few citations adde

Comparison Of Reionization Models: Radiative Transfer Simulations And Approximate, Semi-Numeric Models

We compare the predictions of four different algorithms for the distribution of ionized gas during the Epoch of Reionization. These algorithms are all used to run a 100 Mpc/h simulation of reionization with the same initial conditions. Two of the algorithms are state-of-the-art ray-tracing radiative transfer codes that use disparate methods to calculate the ionization history. The other two algorithms are fast but more approximate schemes based on iterative application of a smoothing filter to the underlying source and density fields. We compare these algorithms' resulting ionization and 21 cm fields using several different statistical measures. The two radiative transfer schemes are in excellent agreement with each other (with the cross-correlation coefficient of the ionization fields >0.8 for k < 10 h/Mpc and in good agreement with the analytic schemes (>0.6 for k < 1 h/Mpc). When used to predict the 21cm power spectrum at different times during reionization, all ionization algorithms agree with one another at the 10s of percent level. This agreement suggests that the different approximations involved in the ray tracing algorithms are sensible and that semi-numerical schemes provide a numerically-inexpensive, yet fairly accurate, description of the reionization process.Comment: 13 pages, 10 figure